The tune to John-O-Dreams may have distant origins, but I heard a recording once of the exact tune, except for the last note of the repeated last line, and the credit was given to two lads from Glenn Miller's trumpet section.

It was on the radio, I was driving, and I've never bothered to verify.
This was just a few years after Bill wrote it.

I suspect that at one stage Bill thought HE wrote the tune, because somewhere I have a song sheet saying "Words and music by Bill Caddick"
Yo carn't trust Brummies nohow!